Genetics of Evolution

Preliminaries

If you are not already familiar with the structure of these exercises, read the Introduction first.

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Contact information

If you have questions about these exercises, please contact Dr. Kevin Middleton (middletonk@missouri.edu) or drop by Tucker 224.

Learning objectives

The learning objectives for this exercise are:

• Describe and identify the mechanisms by which variation arises and is fixed (or lost) in a population over time.
• Model how random mating yields predicted genotype frequencies in Hardy-Weinberg Equilibrium (HWE), and how non-random mating affects allele and genotype frequencies.
• Test whether HWE is present in a population.
• Explain how natural selection and genetic drift can affect the elimination, maintenance or increase in frequency of alleles in a population.

Mechanisms of biological evolution

Evolution is defined by the change in allele frequencies over time. In this context time refers to subsequent generations in a reproducing population. Two main scales of evolution are:

1. Microevolution: both adaptive and non-adaptive (neutral) changes within populations across generations
2. Macroevolution: higher level changes involving origination and diversification of species.

Separating microevolution from macroevolution like this might make it appear that they are completely distinct processes. In reality,

• There is a continuum between the two: microevolutionary change can lead to observable macroevolutionary patterns.
• The fundamental process of change in allele frequencies over time operates the same in both.

One final point to remember is that populations don’t evolve in isolation. Species that live in communities with one another interact with both native and introduced species at many different tropic levels (Figure 1).

Figure 1: In the Galápagos islands, the medium ground finch (Geospiza fortis, upper right) and Galápagos mockingbird (Mimus parvulus, lower left) are both under threat from an introduced nest fly (Philornis downsi, upper left). Simultaneously, these species have unique parasites, a feather mite and feather louse (lower right) that both respond to and impact the evoltionary history of these species. Image from University of Utah

Hardy-Weinberg Equilibrium

If evolution is the change in allele frequencies over time, what defines the lack of change in allele frequencies? In population genetics, no change in allele frequencies is called Hardy-Weinberg Equilibrium (often abbreviated HWE for simplicity). The equations for HWE were developed during the first decade of the 1900’s, shortly after the re-discovery of Mendelian genetics.

HWE allows us to predict genotype (and thus phenotype) frequencies under a specific set of conditions in which there are no additional forces, either internal or external, acting on a population:

1. Infinite population size
2. All mating is random
3. No migration
4. No selection
5. No mutation

There are many processes that can lead to deviations from Hardy-Weinberg Equilibrium.

For each of the conditions above, (1) give an example of a process that would lead to a deviation from HWE and (2) predict whether that process would lead to increased or decreased genetic variation in the subsequent generation.

Evolutionary biologists are often interested in determining if a population is in Hardy-Weinberg Equilibrium. If a population is found to be violating HWE, then it suggests that one of the processes listed above is happening in that population.

Evolution of single alleles

The first phenotypes that you learned about as well as those described in the first set of exercises (Transmission of Genetic Information) were Mendelian traits. In Mendelian traits, a single gene is responsible for a single trait. In this context, you also learned about dominant and recessive alleles (and their variations), which lead to different observable phenotypes.

The simplest case to use for exploring Hardy-Weinberg Equilibrium is a single allele in a diploid organism. In this case, there are only three possible genotypes for two alleles (p and q)¹:

• pp
• pq
• qq

The HWE equation results from the basic rules of probability that you learned about in the first set of exercises. To explore HWE in a population, we will use the example of the Peppered moth (Biston betularia; Figure 2).

(a) Dark morph

(b) Light morph

Figure 2: The Peppered moth (Biston betularia) exhibits two different color morphs, dark and light. These phenotypes are controlled by a single dominant allele p. (a) Individuals with either pp or pq genotypes have the dark morph. (b) Light morphs have the qq genotype.

Imagine a population of Peppered moths with the following allele frequencies:

• p = 0.1
• q = 0.9

There are a few things to note here:

• The frequencies summarize information about an entire population, not about any particular individuals.
• The frequencies sum to 1: either p or q (just like a flipped coin can be either heads or tails).
• The frequencies don’t tell us about whether one allele is dominant.

Probabilities of allele combinations

We can use the rules of probability that you have learned about to determine the probability of an individual having each of the possible genotypes: pp, qq, or pq. Because allele assort independently, the probabilities are just the products of the probabilities.

\[pp = 0.1 \times 0.1 = 0.01\]

\[qq = 0.9 \times 0.9 = 0.81\]

\[pq = (0.1 \times 0.9) + (0.1 \times 0.9) = 0.18\]

Because pq is not distinguishable from qp, we add the probabilities of each combination (0.1 x 0.9 = 0.09 and 0.9 x 0.1 = 0.09).

Either way we add up these probabilities, the sum is 1:

Thus, basic probability leads to the expectation for a population in HWE:

\[p^2 + 2pq + q^2 = 1\]

A population in Hardy-Weinberg Equilibrium will satisfy this equation.

Counts of genotypes

We start with a population of 1,000 Peppered moth individuals, which is large but not infinitely large, that is in HWE. The probability of p is 0.1 and of q is 1 - 0.1 = 0.9. We expect the following genotypes in the population:

Notice that we calculate the probability of q as 1 - p, so we only have to change the value of p.

If each of the individuals makes 10 gametes, then pp individuals will contribute 2 p, pq will contribute 1 p and 1 q, and qq individuals will contribute 2 q.

We will have the following numbers of alleles represented and resulting frequencies of p and q in the next generation.

In the first code block above, iteratively change the values of pop_size and p. Start by leaving p at 0.1 and change pop_size to larger or smaller values. Run the first code block and then the second. See how the frequencies of p and q change. Then set pop_size to 1000 and change the value for p to some number between 0 and 1.

How do the final values for <i>p</i> and q change as you change population size? How do the final values for p and q change as you change the starting probability of p?

Testing HWE chisq

Example of MM mice

Evolution of polygenic traits

Counting the ways that alleles can combine (coins)

Figure 3: Allelic combination plot for 1 gene. There is a 1:2:1 (TT:AT:AA) ratio of two alternate alleles at a single position in the genome. There are 4 possible combinations (just like for two coin flips). The counts of each set of combinations are shown with the red number at the top of the bars. The y-axis shows the relative percentage of each.

Mechanism of selection

- Moving population average
- Drift vs. selection

• Effect of sample size on selection and drift in phenotypic evolution
  • Drift as sampling error
  • Drift has a larger effect in small populations

Populations have significant underlying variation

Intuition of moving mean

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References

Footnotes

1. p and q are most commonly used as the allele names, but you could substitute any pair: A and B, A₁ and A₂, etc.